complex analysis

Question

if lim_n→∞ z_n = A ,prove that 

lim_n→∞ (z₁+z₂+...........z_n) = A

 

please help me sir please

Answer 1

The correct statement is that if lim_{n to infinity} z_{n}=A then the average sequence (z_{1}+z_{2}+..._z_{n})/n also converges to A as n goes to infinity. To find a proof of this fact just google Cesaro mean of a sequence.